In order to raise the temperature of 5.0 Kg of water from 20 deg. C to 30 deg. C, a 2.0 kg iron bar is heated and then dropped into the water. What should the starting temperature of the bar be? (Specific heat Fe is 0.22 cal/g-deg.)
I may have answered this for you already but here it is again.
heat lost by Fe bar + heat gained by water = 0
[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for spcific heat Fe, the only unknown.
To find the starting temperature of the iron bar, we can use the principle of conservation of energy. The energy gained by the water should equal the energy lost by the iron bar.
The energy gained by the water can be calculated using the formula:
Energy gained by water = mass of water × specific heat of water × change in temperature
Given:
Mass of water (m₁) = 5.0 kg
Initial temperature of water (T₁) = 20 deg. C
Final temperature of water (T₂) = 30 deg. C
Specific heat of water (Cw) = 1 cal/g-deg.
Let's calculate the energy gained by the water:
Energy gained by water = (mass of water) × (specific heat of water) × (change in temperature)
= (5.0 kg) × (1 cal/g-deg.) × (30 deg. C - 20 deg. C)
Now, let's calculate the energy lost by the iron bar:
Energy lost by iron bar = (mass of iron bar) × (specific heat of iron) × (change in temperature)
= (2.0 kg) × (0.22 cal/g-deg.) × (T₁ - 30 deg. C)
Since the energy gained by the water equals the energy lost by the iron bar, we have:
(mass of water) × (specific heat of water) × (change in temperature) = (mass of iron bar) × (specific heat of iron) × (change in temperature)
(5.0 kg) × (1 cal/g-deg.) × (30 deg. C - 20 deg. C) = (2.0 kg) × (0.22 cal/g-deg.) × (T₁ - 30 deg. C)
Now, let's solve for T₁, the starting temperature of the iron bar:
(5.0 kg) × (10 deg. C) = (2.0 kg) × (0.22 cal/g-deg.) × (T₁ - 30 deg. C)
50 kg-deg. C = 0.44 kg-cal/g-deg. × (T₁ - 30 deg. C)
Dividing both sides by 0.44 kg-cal/g-deg.:
(50 kg-deg. C) / (0.44 kg-cal/g-deg.) = T₁ - 30 deg. C
Simplifying:
113.64 deg. C = T₁ - 30 deg. C
Adding 30 deg. C to both sides:
T₁ = 113.64 deg. C + 30 deg. C
T₁ = 143.64 deg. C
Therefore, the starting temperature of the iron bar should be approximately 143.64 deg. C.